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6.68 Use Table II to obtain each shaded area under the standard normal curve.

Short Answer

Expert verified

a.0.9500

b.0.9802

c.0.2006

d.0.1010

Step by step solution

01

Part (a) Step 1: Given Information

The given graph is:

02

Part (a) Step 2: Explanation

Subtracting the smaller area from the bigger area yields the area under the normal curve between two specified z-scores.

There is an area between two z-scores equal to the larger of the two supplied areas minus the smaller of the two given areas.

Thus, the area under the standard normal curve to the left of 1.96 is 0.9750, whereas the area under the standard normal curve to the left of -1.96 is 0.0250.

As a result, the area between -1.96and 1.96under the usual normal will be 0.9750-0.0250=0.9500.

So, the shaded area is0.9500

03

Part (b) Step 3: Given Information

The given graph is:

04

Part (a) Step 2: Explanation

Subtracting the smaller area from the bigger area yields the area under the normal curve between two specified z-scores.

There is an area between two z-scores equal to the larger of the two supplied areas minus the smaller of the two given areas.

Thus, the area under the standard normal curve to the left of 2.33is 0.9901, whereas the area under the standard normal curve to the left of -2.33is 0.0099

As a result, the area between -2.33and 2.33under the usual normal will be 0.9901-0.0099=0.9802

So, the shaded area is0.9802

05

Part (c) Step 5: Given Information

The given graph is:

06

Part (c) Step 6: Explanation

To the left of -1.28, the area under the standard normal curve is 0.1003.

Areatotheright=1-Areatotheleft

To the left of 1.28,the area under the standard normal curve is0.1003.

1-0.8997=0.1003is the area to the right of1.28.

As a result, the area beneath the standard normal to the left of -1.28and to the right of 1.28will be 0.1003+0.1003=0.2006.

07

Part (d) Step 7: Given Information

The given graph is:

08

Part (d) Step 8: Explanation

To the left of -1.64, the area under the standard normal curve is 0.0505

Areatotheright=1-Areatotheleft

To the left of -1.64, the area under the standard normal curve is 0.94950.9495.

1-0.9495=0.0505 is the area to the right of 1.64

As a result, the area beneath the standard normal to the left of-1.64and to the right of1.64will be0.0505+0.0505=0.1010.

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